IAEA-TECDOC-1139
XA0054838
Transient and accident analysis of a BN-800 type LMFR
with near zero void effect
Final report on an international benchmark programme supported by the International Atomic Energy Agency and the European Commission
1994-1998
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TRANSIENT AND ACCIDENT ANALYSIS OF A BN-800 TYPE LMFR WITH NEAR ZERO VOID EFFECT
IAEA, VIENNA, 2000 IAEA-TECDOC-1139
ISSN 1011-4289
FOREWORD
Large conventional liquid metal cooled fast reactor (LMFR) cores show a significant reactivity increase if a coolant loss occurs by boiling or gas intrusion. Since this positive reactivity effect is very important for the overall behaviour of LMFRs from a safety point of view, a lot of attempts have been undertaken worldwide to reduce the sodium void reactivity effect (SVRE).
One proposal has been made by the Institute of Physics and Power Engineering (IPPE), Obninsk, Russian Federation, in which the core upper axial blanket is replaced by a sodium plenum consisting of sodium filled wrapper tubes. In this case the enhanced axial neutron leakage would result in a strong negative reactivity effect in case of sodium voiding which would compensate a large fraction of the positive SVRE in the core region. The International Atomic Energy Agency (IAEA) and the European Commission (EC) Joint Benchmark Programme have assessed the capability of reducing the SVRE of such innovative core design.
The analysis (IAEA-TECDOC-731, 1994) showed that overall SVRE for the reference 2100 MW(th) MOX fuel core might be close to zero.
This method of reducing the SVRE has been adopted in the BN-800 reactor design in the Russian Federation. However, investigations were needed to determine differences in severe accident responses in order to estimate the feedback to overall safety that could be achieved by a reduction in the SVRE value for MOX fuel reactor core.
Therefore, recognizing the importance of such an innovative LMFR core design, a comparative exercise of severe accidents for BN-800 type reactors with reduced sodium void coefficient was jointly initiated by the IAEA and the EC in 1994. The Russian specialists took over the task to prepare the benchmark input data, a revised draft of which was distributed by the IAEA to the participants at the end of June 1995. The specifications of the benchmark were finally fixed in a meeting at the IAEA in Vienna on 11-13 December 1995.
The main findings resulted from intensive discussions through eight IAEA/EC joint meetings held in turn in Vienna and Brussels. The final meeting was held at IPPE, Obninsk, Russian Federation, on 2-6 June 1998. The benchmark programme resulted in an effective information exchange among the Member States sharing requirements as well as experience in advanced reactor design and computer codes for transient calculations.
This report, which describes the results of the benchmark programme, was co- ordinated by J. Kupitz, IAEA and G. van Goethem, European Commission. The IAEA officer responsible for this publication was A. Rineiskii, of the Division of Nuclear Power.
The IAEA wishes to express its appreciation to all those who participated in the benchmark programme which is a good example of the joint IAEA/EC research activities for LMFR development. Valuable contributions to the benchmark exercise have been made, in particular, by D. Struwe (FZK, Karlsruhe, Germany), LA. Kuznetsov (IPPE, Obninsk, Russian Federation), J.M. Frizonnet (IPSN, Cadarache, France), H. Niwa (JNC, O-arai, Japan) and Om Pal Singh (IGCAR, Kalpakam, India). D. Struwe acted as Chairman throughout the joint meetings.
EDITORIAL NOTE
The use of particular designations of countries or territories does not imply any judgement by the publisher, the IAEA, as to the legal status of such countries or territories, of their authorities and
institutions or of the delimitation of their boundaries.
The mention of names of specific companies or products (whether or not indicated as registered) does
CONTENTS
Summary...!
CHAPTER 1. SYNTHESIS OF NEUTRON PHYSICS CALCULATIONS...^
1.1. Russian calculations... 15
1.1.1. Methods and calculational models... 15
1.1.2. Results of calculations...21
1.2. Italian calculations...25
1.2.1. Introduction...25
1.2.2. Results of calculations...28
1.3. Japanese calculations ...51
1.3.1. Introduction...51
1.3.2. Results of calculations...52
1.4. Comparative analysis of neutronics calculations...56
1.5. Conclusions...60
References to Chapter 1 ...70
CHAPTER 2. EVALUATION OF STEADY STATE CALCULATIONS OF THE FUEL PIN BEHAVIOUR DURING POWER OPERATION IN A BN-800 LIKE REACTOR CORE...71
2.1. Introduction...71
2.2. Basis of the calculations...71
2.2.1. Case set-up...71
2.2.2. Characterization of the applied fuel pin mechanics code packages ...78
2.3. Summary of results...80
2.3.1. Fuels thermal behaviour...80
2.3.2. Fuel to clad heat transfer ...84
2.3.3. Fission gas release during power operation ...88
2.4. Conclusions and recommendations...88
References to Chapter 2...91
CHAPTER 3. PREBOILING ANALYSES OF ULOF ACCIDENTS ...93
3.1. Introduction...93
3.2. Computer codes used...93
3.3. Results...95
3.3.1. Base case...95
3.3.2. Parametric case...99
3.3.3. Uncertainties in core physics data...100
3.4. Conclusions... 104
References toChapter 3... 104
CHAPTER 4. BOILING AND POST FAILURE ANALYSIS RESULTS OF ULOF ACCIDENTS ... 109
4.1.2. Parametric case results... 122
4.2. Core configuration at the end of the initiating phase... 143
4.3. Conclusions... 148
CHAPTER 5. TRANSIENT ANALYSIS RESULTS OF UTOP AND UTOP/ULOF ACCIDENTS...151
5.1. Introduction...^! 5.2. Basis of the calculations...151
5.2.1. Case set-up... 151
5.2.2. Codes applied... 152
5.3 Transient results for the fast UTOP (0.5$/S)...153
5.4. Transient results for the slow UTOP (0.05$/S)...162
5.5. Transient results for the UTOP-ULOF accident...170
5.6. Conclusions and recommendations...190
References to Chapter 5... 191
CHAPTER 6. PHYSICS PARAMETERS OF PARTIALLY DESTROYED CORE CONFIGURATION... 193
6.1. Calculation model and analysis methods...193
6.2. Integral reactivity effects...197
6.3. Doppler effect...203
6.4. Reactivity of materials (2100 K)...203
6.4.1. Sodium integrals of reactivity and space distribution...203
6.4.2. Steel worth...216
6.4.3. Fuel worth...228
6.5. Reactivity effects caused by material expansion...228
6.6. Neutron kinetics functionals ...229
6.7. Conclusions...241
List of participating organizations and participants...243
SUMMARY
1. INTRODUCTION
Research on liquid metal fast reactors (LMFRs) during the last decade has significantly improved the understanding of the fast reactor issues. This forms the basis for the development of safety analysis methods and codes which are necessary to evaluate the safety characteristics of existing and new fast reactor core and plant designs and to optimize safety and operational procedures. In spite of all the progress made on the safety issues, the quest for excellence calls for further work. One of these issues is the positive sodium void reactivity effect of large size reactors. There is a strong incentive to search for core designs, which have a considerably reduced positive sodium void reactivity effect.
One idea followed by Russian scientists has been to investigate the suitability of reducing the integral sodium void reactivity by an axially heterogeneous core design with a sodium plenum region just above the fissile core region instead of the upper axial blanket. A first benchmark exercise on this subject was jointly organized by IAEA and EC. It was mainly devoted to the involved reactor physics issues under normal operation conditions. It could be demonstrated that the integral sodium void effect of a MOX fueled LMFR of the 2100 MWth class could be reduced to a value of nearly zero (IAEA-TECDOC-731). After finalization of this benchmark exercise it was clear that further investigations are needed to determine the transient response of such a design to severe accidents including those which could lead to core destruction. Such investigations form the basis for estimations to what extent a reduction of the positive void worth could contribute to a further reduction of the residual risk of LMFRs.
At the meeting of the IAEA's IWGFR in May 1994, a comparative exercise for a severe accident in a BN-800 type reactor with a near zero void innovative core was proposed by the Russian Federation. This proposal was endorsed by all the countries and the EC. The organizations participating in the comparative exercise are: FZK from Germany, IPSN from France, AEA-T from the UK, ENEA from Italy, PNC and HITACHI from Japan, IGCAR from India and IPPE from the Russian Federation A variety of specialists from the participating organizations contributed to the comparative exercise.
The comparative exercise was organized on different stages. These different stages
covered the following items:
Stage 7:Case set-up covering core and plant design characteristics, the preparation of the neutron physics input data, the specification of thermal-hydraulic design values and the specification of the fuel loading scheme during power operation.
Stage II: Determination of the fuel pin state at the end-of-equilibrium-cycle (EOEC)-conditions taking into account the power operation history appropriately.
Stage III: Analysis of preboiling transients of the ULOF-accident by considering or not
reactivity feedback related to the structures heat-up. Effects of load pad expansion and control
rod drive line expansion were considered in detail.
Stage V: Analysis of post-failure transients up to a core state at which larger parts of the core were destroyed and at which hexcan failures are to be expected.
Stage VI: Analysis of other initiators for core destruction as unprotected reactivity accidents leading to a transient overpower accident (UTOP). Three types of initiators were considered : an 0.5 $/s reactivity ramp rate, an 0.05 $/s reactivity ramp rate and a structured reactivity ramp rate superimposed by a loss of flow. These kind of accidents have some importance in residual risk studies performed for the BN-800 type reactor.
Different tools were applied by the different participants to the exercise. However, not all participants contributed to each stage. Main results of the different stages of the exercise are presented here in a concise manner. The main findings resulted from intensive discussions between the partners at eight Consultants Meetings organized by the IAEA.
2. RESULTS OF ANALYSES 2.1. Case set-up
The Institute of Physics and Power Engineering (IPPE) from Obninsk provided the necessary information on the case set-up. The given data are representative of a 1500 MW(th) reactor design with above core sodium plenum, as in BN-800 reactor core design. The central part of the reactor comprises the core, the primary shielding and the spent fuel assembly storage. The core and the blanket hexagonal fuel assemblies are inserted into the inlet header collector hole which is located at the reference height of 0.1 m. The radial blanket height is 1.84m and it comprises one row of 84 subassemblies surrounding the core. The primary shielding steel hexagonal are arranged with the same spacing as the one of core fuel elements.
The core consists of 511 cells, 481 of which are filled with fuel subassemblies and 30 are intended for control, safety and shutdown rods. For radial flattening of the power production the core is divided into three different enrichment zones: the central low enrichment zone (LEZ) consisting of 181 subassemblies, the intermediate medium enrichment zone (MEZ), consisting of 138 subassemblies and the peripheral high enriched zone (HEZ) consisting of 162 subassemblies.
The fuel pin height consists of a 0.67 m long lower fission gas plenum followed by a 0.35 m long lower axial breeder zone. Fissile core height amounts to 0.84 m only followed by a 0.05 m long end cap region which acts as an upper axial reflector. Above this there is a sodium plenum of 0.35 m length followed by a 640 shield of 0.25 m length. Fissile pellets are hollow pellets with chamfered edges. Fertile pellets are without chamfers. The total mass of fuel in the core amounts to 11668 kg. The cylindrical equivalent fissile core radius amounts to 1.1869 m.
Fertile pellets of the radial blanket assemblies are fat solid pellets of depleted uranium oxide.
Coolant entering the inlet header of the reactor is distributed in between the following main areas: the core, the radial blanket, control absorber rods, the inner and outer radial shield and the spent fuel storage. Besides, some part of the coolant through subassembly foot penetrates into the inter-subassembly space and is discharged into the upper outlet plenum of the reactor. For flattening of the coolant outlet temperature distribution, hydraulic shaping is performed by means of appropriate choices of the hydraulic resistance of subassembly inlet devices. The total coolant mass flow through the core is 6027 kg/s. With a core inlet
gas plenum amounts to 0.59 MPa with a pressure drop along the highest powered fuel pin bundle length of 0.302 MPa and along the lower subassembly tail and the pin bundle inlet of 0.11 MPa. If the plant's power supply gets lost and one assumes that the diesels of the emergency power supply system do not start as expected, the primary pumps begin to reduce their rotation speed by the law of free coast down. The halving time amounts to 5.5 s, i.e., the coolant mass flow gets reduced rather rapidly. The secondary sodium flow rate changes in time accordingly. However, the sodium inlet temperature will start rising smoothly only after 180 s into the transient.
The reactor is designed to operate on a three batch reloading scheme, with a total residence time for a particular subassembly of 420 equivalent full power days (i.e. three cycles, each of length 140 days). Subassemblies in the radial breeder zone have a residence time of 490 days. For determination of the local variation of the power and the reactivity feedback effects in the different enrichment zones, these are subdivided into representative subassembly groups (SAGs), four groups for the LEZ and three each for MEZ and HEZ, respectively. Each of the SAGs are subdivided into one third portions representing the three batch loading scheme. The radial breeder is represented by one SAG. In axial direction 12 zones have been chosen to simulate the axial profiles of power and reactivity feedback coefficients appropriately. As a consequence of this core representation, the reactor core is simulated with 30 SAGs and 10 radial zones for representation of neutron physics parameters in the fissile core region.
Evaluation of the neutron physics parameter of the core set-up was performed by IPPE from Obninsk, by ENEA from Italy and by HITACHI from Japan. The Russian evaluation of reactivity coefficients was based on tools using first order perturbation theory in 26-group diffusion theory. The calculations have been made using the standard version of the BNAB-78 data base applying the ARAMAKO-S system for preparation of the cross sections. In order to evaluate the effect of the use of different cross section libraries, some calculations were performed using a modified version of the RHEIN set developed in the framework of the former USSR — GDR bilateral co-operation. All these calculations were done in R-Z geometry. To evaluate the validity of the use of the first order perturbation theory, complementary calculations were performed with the 26-group SYNTEZ code and the 3D TRIGEX code with an 11-group representation. The ENEA calculations covered 2D and 3D representations of the core geometry. Due to the heterogeneous character of the core design, it was felt that a 3D representation was essential. The CITATION code was applied using a 22- group cross section library originating from the ENDF/B - V.II file. In addition, transport theory in a 3D hexagonal full core representation was provided for evaluation of the sodium void effect. The MCNP4A Monte Carlo Transport code was used. HITACHI performed both diffusion and Monte Carlo transport calculations in R-Z and Hex-Z configurations using the latest Japanese nuclear data library JENDL-3.2.
Comparison of the results of neutron physics calculations performed by the participants to this part of the exercise let to the following conclusions:
• The power distributions were in good agreement with each other with maximum deviations in integral results of only 2% and up to 4.1% deviations if local values of linear ratings were considered.
• The kinetics parameters were in satisfactory agreement with each other.
These differences became larger for the voided core configurations. They were attributed to differences in cross-section libraries and more importantly to the selected range of temperatures forming the basis for the evaluation. In addition, it turned out that the amount of changes of the Doppler coefficient in case of voiding depends in a non negligible manner on the local void pattern along core cross section.
• The sodium void reactivity effect was calculated rather close to each other by the different participants. The largest differences in integral values amount to about 20%. However, each of the calculations has demonstrated that integral results are rather dependent on the local pattern of voiding and it is difficult to argue on the conservatism of an approach without detailed evaluations. An important impact of the use of higher order methods has been observed consistently by all participants to this part of the exercise. Similarly coherent were the results that appropriate consideration of fission products becomes essential when calculating the sodium void effect dependent on the residence time of subassemblies. Common to all results was that the sodium void effect amounts to 4.5 $ if all positive contributions are summed up. The void effect of the fissile core region amounts to 2.7 $ and the one of the upper sodium layer to —3.3 $. The integral sodium void effect sums up to a considerably negative value of-0.6 $.
• The steel reactivity feedback effect of the core region amounts to 5.2 $ which included the clad and hexcan material.
In addition to the neutron physics parameters of the as designed core geometry, analyses were performed by IPPE on the influence of the core materials relocation on the neutron physics parameters. In this regard, core configurations considered are: sodium void inner the two enrichment zones, clad material accumulated partly at the upper end of fissile core height and dominantly around the lower end of fissile core height, i.e. at the boundary of the lower axial blanket. Such a configuration can only be achieved when the clad material and the fuel is heated up considerably. The analyses indicated a relatively little impact of distorted core configuration on the sodium void worth distribution but a large effect on Doppler reactivity feedback. The influence of these findings on transient analyses results could not be evaluated.
Common conclusions of this part of the exercise are that higher order methods have a considerable effect on sodium void worth effect, local patterns of voiding have a different effect on the integral value than determined from differences of unavoided and fully voided core configuration and core materials relocation seem to influence the Doppler feedback considerably. All these findings indicate that it might become necessary to apply space time neutronics methods for the transient analyses when aiming at a considerably higher precision in the transient analyses than the one achieved with currently available methods and data base.
2.2. Fuel pin characterisation at EOEC-conditions
Five countries participated to this stage of the exercise with different code systems: The Russian Federation with their KONDOR code package, France with the GERMINAL code, United Kingdom with the TRAFFIC code, Germany with the DEFORM-4C code package as part of the SAS4A code and India with the PINCH code package. The different codes applied in this comparative exercise cover the whole spectrum of currently available model capabilities ranging from detailed deterministic model approaches realised in codes such as GERMINAL
Comparison of results provided by the partcipants to the exercise up to the 5th Consultants Meeting, December 1996 in Vienna led to the following conclusions:
• Results of the PINCH calculations for gap conductance compare well with other code predictions. Calculated values of the fractional fission gas releases are high and relatively low fuel temperatures are calculated. Review and refinement of the chosen approach is strongly recommended.
• Results of the TRAFFIC code calculations are difficult to compare to the results of the other participants because differences are mainly determined by the power history differently simulated for the 420 days power operation time and the simulation of a clad material which leads to a low clad swelling even for high doses. However, differences of the results to the ones of the other calculations are clearly explained by the different assumptions taken in the case set-up which were agreed upon at an early stage of the exercise.
• Results of the KONDOR, GERMINAL and DEFORM-4C calculations are relatively close to each other. However, differences in between the calculations become more pronounced when medium burnup levels of about 5 at% are exceeded. It appears as if more refined modelling approaches need to be developed for the KONDOR code system for an improved description of the fuel pin mechanics behaviour approaching high burnup levels of 8 to 10%
at% and low linear ratings. Differences between DEFORM-4C and GERMINAL calculations evolve partly from different approaches to simulate JOG-formation and the respective behaviour during power operation. This is a topic of the current research and development activities in this field, which needs more refined analyses and model development and most importantly a broader experimental data base.
For evaluation of the reliability of the provided code predictions about the performance of the BN-800 fuel pins under power operation, it would be necessary to compare calculated results with experimental results for the specific BN-800 fuel pins considered in this exercise.
This holds especially for results provided on the basis of parametric modelling approaches of DEFORM 4C. Impact of fuel fabrication and clad material properties variation with burnup can only be evaluated based on detailed experimental results. This was not the objective of this comparative exercise. However, it is strongly recommended that results should be compared in more depth with the experimental data base available in the Russian Federation from power operation of respective fuel pins in the BN-350 and the BN-600 reactors.
For the purpose of this exercise, comparison of results has shown that the calculated fuel pin states at the EOEC are rather close together. Therefore transient calculations start from initial conditions sufficiently close to each other so that possible differences in the transient calculations should not be dominated by differences in the state fuel pin characterisation after power operation. However, differences are to be expected between the transient calculations of the Russian Federation and India on the one side and the ones of France, Japan and Germany on the other side. This is due to the fact that fuel pin mechanics code packages are not applied during the transient calculations by the Russian Federation and India but they are consistently used in the calculations by the other three participants in the further stages of the exercise. This results in an important difference in the simulation of the further accident progression. The first two participants assume the heat transfer coefficient between fuel and clad is constant in time at a level evaluated at the end of the power operation in steady state. The other three participants
Some differences in transient calculations are to be expected between the contributions from France and Japan on the one side and Germany on the other side because Germany applied a code version of DEFORM-4C for transient calculations which has been improved since December 1996 as compared to the one used by France and Japan.
2.3. Analyses of preboiling transients of the ULOF-accident
Five countries contributed to this stage of the exercise namely the Russian Federation, India, Japan, France and Germany. The Russian Federation applied their GRIF-SM code system, which calculated in great detail the thermal-hydraulics core behaviour and simulates the primary and secondary circuit behaviour of the BN-800 type reactor appropriately. Interwrapper sodium flow is simulated. However, the fuel pin behaviour considers the thermal behaviour appropriately but it does not calculate the transient fuel pin mechanics behaviour and hence applies axially variable but transiently constant gap heat transfer coefficients. India applied their PINCHTRAN code package, which accounts reactivity feedback effects in single phase comprehensively and sodium boiling is simulated similarly to the SAS1A model. Such a representation is felt too simplified for the simulation of two phase flow conditions. The transient fuel pin mechanics behaviour is not modelled. The primary and secondary circuit behaviour is simulated in a simplified manner. Japan, France and Germany applied slightly different code versions of the SAS4A-code being very close to the REF96.Rell.O code version.
The French participant improved the sodium EOS in the post failure module and introduced mechanical properties of 15/15 Ti stabilized cladding. The German participant modified and improved the fuel pin mechanics model and the two-phase flow boiling model. The Japanese participant modified clad motion model to avoid the formation of the steel accumulation at the fissile top and thus extended the applicability of the model. They contributed to the exercise with the actually available most recent code versions to introduce the newest state of knowledge into the discussion of results. The representation of the BN-800 subassemblies is rather detailed.
The primary and secondary circuits are simulated only approximately in the framework of a scaled-down LSPB plant design.
The calculations performed can be subdivided into three classes: (A) Base case calculations neglecting reactivity feedback effects as a consequence of the core structures heat- up and applying the reference neutron physics data. (B) Uncertainty analyses of the neutron physics input data, and ( C ) Consideration of different reactivity feedback effects due to core structures heat-up as radial core expansion and control rod drive line expansion. However, it seems appropriate to mention here that intensive discussions took place on the question whether there is sufficient evidence from theoretical and/or experimental investigations to argue that the efficiency of radial core expansion under the given conditions can be regarded as verified. On the background of experiences gained with respective analyses for FFTF, Phenix and Super-Phenix, it was decided to neglect this reactivity feedback effect totally. However, it was not possible to arrive at a uniquely accepted position. Therefore, it was agreed to consider the respective calculations as optimistic parametric cases.
On the basis of the results, the following conclusions can be drawn:
• The heat-up of the upper sodium layer leads to a negative reactivity feedback contributions related to the sodium heat-up in the fissile core region. The normalised power therefore decreases continuously after onset of the coolant mass flow decrease. However, boiling
• In the class (A) calculations, all participants predict boiling onset in the highest powered MEZ core region about 16.7 up to 18.9s into the transient. The normalised power level has decreased down to 71% to 63% of its nominal value. Up to this time into the transient, reactivity feedback effects remain quite small but differences in between the different calculations are observed which are related to different model assumptions on the calculation of fuel pin axial expansion.
• In the class (C ) calculations, boiling onset is calculated in the highest powered MEZ core region as well but only at 28.9s to 33.2 into the transient when the normalised power has been reduced to a value of about 44% to 39% of its nominal value. Up to this time, the radial core expansion reactivity feedback amounts to about -0.43 $.
These results indicate that the negative value of the of the sodium void reactivity is well suited to be identified as a passively activated safety measure which compensates potential difficulties which might arrive from the design feature of a quite rapid coolant mass flow reduction curve in the case of loss of offsite power and delayed availability of the emergency power supply.
2.4. Boiling and post-failure transients as a consequence of a ULOF-accident initiator Five countries participated to this stage of the exercise namely the Russian Federation, India, Japan, France and Germany. The Russian Federation and India contributed with their GRIF-SM and PINCHTRAN code packages providing the capability to follow the transient behaviour up to peak cladding temperatures of 1500 K. For later phases of the accident the code packages cannot be applied because it does not provide models to describe consequences of clad and fuel relocation after clad melting onset. France, Germany and Japan used the SAS4A code, which was developed by these countries in the last 10 years in close co-operation starting from the code version provided by the US/DOE in 1986/88. The code versions used by these three partners are based on the identical version SAS4A REF96 Rell.O, but each participant performed some modifications independently in order to apply it to this reactor successfully.
In principle, calculations can be grouped into two classes again:
• continuation of the class (A) calculations of stage III of the exercise (base case evaluations). Evaluations of these cases were complemented by analyses of consequences of an early loss of fission gases from the upper fission gas plena by Japan. As it turned out that this effect does not modify the integral event sequence drastically, it was agreed to neglect this effect in the bulk of the analyses. However, it is felt reasonable and necessary to re-evaluate the case when more reliable results than here are to be provided, i.e. if it would come to licensing of the reactor design.
• continuation of the class (C) calculations of stage III of the exercise, again neglecting the effect of an early fission gas release from the upper fission gas plena (parametric case evaluations).
Both kinds of analyses were performed using nominal reactivity feedback coefficients for Doppler, sodium void, fuel pin expansion, clad motion and fuel motion. In most of the considered cases the reactivity feedback effect of the expansion of the control rod drive lines are
Base case results: The negative reactivity feedback contribution due to the voiding of the upper sodium layer is a quite efficient measure to mitigate the impact of the positive reactivity feedback contribution when the coolant along fissile core height is voided. Along the first 2 s of the boiling transient, the normalised power decreases to a value of about 0.4 to 0.5. However, during the next 4 s, the net reactivity increases again to about delayed critical and the power increases to a value of about 0.6 to 0.7 nominal. The subsequent boiling development releases negative reactivity but this is partially compensated for by positive contributions related to clad material relocation. During the next 2 s, the sodium reactivity feedback becomes again positive being considerably enhanced by an increasingly positive reactivity feedback due to clad material relocation. The net reactivity becomes positive, driving the normalised power to nominal values and beyond. This mild power transient leads to fuel pin breakup in the high powered subassembly group of the medium enrichment zone. The subsequently calculated fuel relocation initiates a slow but gradually proceeding reactor shut down. Most of the fissile core channels are voided and the void reactivity has reached or exceeded its saturation value of about - 0.6$. Clad relocation continues but heat-up of the hexcan wrapper structure melts. Further core material phenomena will deviate considerably from the quasi-one-dimensional behaviour in the initiation phase. It can be concluded that the accident will enter into the transition phase. The ULOF-transient is not at all finished at the end of the calculations. Achievement of permanent subcriticality or in-place coolability of the partially destroyed core could not be demonstrated.
Parametric case results: The event sequence calculated for the case where radial core expansion is considered are genetically very close to the results of the base case. However, time scales of the crucial events are longer and the respective power levels smaller during the boiling transient time period. Clad relocation cannot be prevented and it is this positive reactivity feedback together with some contribution from sodium boiling which drives the normalised power back to nominal values and above which then initiates a mild power transient leading to fuel pin breakup and a post-failure transient which is only little different from the one calculated for the base case. This accident enters similarly well into a transition phase which needs to be analysed carefully.
The Russian Federation analysed one further parametric case in which radial core expansion and control rod drive line expansion were considered. As a consequence of these two structure reactivity feedback effects, boiling onset is delayed and clad dry out is not predicted up to 100s of the transient. On the basis of this calculation, it was concluded by the Russian participant that long term coolability could be established if the structure feedback is sufficiently strong and becomes activated in due time. The other participants did not agree to this conclusion. First of all, it was felt necessary to continue the calculation beyond times at which the reactor coolant inlet temperature starts rising. Secondly it was felt overly optimistic to superimpose the reactivity feedback due to radial core expansion and control rod drive line expansion. Thirdly it was felt necessary to evaluate consequences of the transient, by considering variation of the fuel to clad heat transfer coefficient. This last item could have been evaluated only if calculations with a SAS4A-type of code would have been performed. The other participants were not in a position to do so because it would have needed a thorough review of the approach to simulate the primary and secondary circuit behaviour for these long lasting transients within the SAS4A code frame. However, this was not the purpose of the comparative exercise and the effort to do so was too large to be covered within the scope of this exercise.
not yet demonstrated that this innovative core design leads only to benign consequences in terms of thermal and mechanical loading of structures of the primary system.
2.5. Consequence and analyses of other initiators for core destruction (UTOP, UTOP/ULOF)
Four countries participated to this state of the exercise namely the Russian Federation, India, France and Germany. However, contributions from the first two partcipants were only of limited value because their code systems do not provide information on the transient fuel pins behaviour. They do not provide the capability to calculate fuel pin failure conditions mechanistically and they do not provide information on consequences of core materials relocation after fuel pin failure other than to impose a pre-specified materials relocation behaviour which is not adequately representing the reality and which does not represent the current state of knowledge and technology. Therefore, discussion of results hereafter is mainly based on calculated results provided by the last two participants. At this stage of the exercise two classes of accident initiators were considered:
• Consequences of unprotected reactivity ramp rate accidents leading to a UTOP-accident.
Two types of reactivity ramp rates were considered in detail: an 0.5$/s reactivity ramp rate and an 0.05$/s reactivity ramp rate. For both cases, impact of the reactivity feedback of radial core expansion on the event sequence was neglected and nominal values of the other reactivity feedback coefficients were used.
• Consequences of an accident scenario with unprotected withdrawal of 6 compensator rods from the core accompanied by failure of all scram system absorber rods and initiation of a loss-of flow. The externally supplied reactivity was limited to a maximum value of 3.9 $.
This accident initiator leads to a so called UTOP/ULOF accident. It is of some interest for the evaluation of the residual risk associated with the operation of a BN-800 type reactor.
Boundary conditions of the calculations are the same as for the previously mentioned analyses.
Calculated results of the pure UTOP analyses
To perform these calculations it was necessary to get access to experimental data of the BN-800 clad material properties. These should give insight into the relations between temperatures and strain rate on the one side and ultimate tensile strength and yield stress on the other side. Most importantly, experimental data on the respective failure strain values are necessary. In addition variation of these data with accumulated doses are necessary. The information could be provided only partially. The strain rate dependency could not be given as well as the failure strain dependencies of the irradiated clad material. Analyses were therefore performed with material property functions deduced in the framework of the CABRI experimental programme for a 20% coldworked 15/15 Ti stabilised clad material. This was done under the assumption that the BN-800 clad material behaves similarly. However, this is a quite risky procedure because extrapolation of clad material properties for irradiated clad represents a very difficult subject and definitely needs experimental backup. Thus, the results presented and discussed here can only be of a preliminary nature. This concern is to be taken seriously because information on material properties for the BN-800 clad material at high dose loads revealed that the material properties are considerably different than the ones assumed in
Results of the slow reactivity ramp rate calculations are sensitively dependent on the transient variation of contact pressures at the fuel to clad interface and on the balance of fuel melt cavity pressure buildup and the transient radial expansion of the still solid fuel. It is due to this fact that the calculation presented by France, calculates firstly boiling onset though the calculation presented by Germany predicts fuel pin failure prior to boiling onset. In both cases fuel pin failure is calculated in one subassembly group (SAG) at 3 6S to 41s of the transient, at 67% to 79% of the core height and when a failure strain of 1.7% or 0.5% becomes exceeded. At this point in time, the normalised power has reached about 3.1 times the nominal value which corresponds to a peak linear rating in the concerned SAG of about 1050 to 1100 W/cm. The two reliable calculations for this case have shown that failure conditions depend strongly on details of the fuel pin mechanics simulation and most pronouncedly on the actual established strain rate.
In the calculation presented by Germany, first fuel pin failure occurs at a time of the transient when heat-up of the fuel pins and clad straining in several SAGs results in liquid sodium displacement from central core regions. Therefore, it leads to a transient increase of the integral sodium reactivity feedback just prior to failure prediction. After failure, sodium is displaced additionally at the failure site by the ejected fuel. The cumulative effect of these reactivity feedbacks result in a slight increase of the power which is considerably reduced, with a time delay of about 170 ms, when dispersal initiates a rapid reactor shutdown.
When sodium boiling takes place before pin failure the post failure transient looks slightly different, but at the end of the calculations partial blockage formation in the concerned SAG leads to a core configuration which can hardly be cooled in-place on a long time scale. The accident most probably will enter into a slow core melt down with a progressive core destruction by a thermally induced subassembly to subassembly propagation.
Results of the rapid reactivity ramp rate calculations reveal a similar sensitivity against details of the simulation of the fuel pins mechanical behaviour and against actual strain rate dependencies of the clad material properties. These details influence the coolant heat-up considerably thus establishing transient conditions where fuel pin failure is calculated to occur either prior to boiling onset or only afterward with some time delay. If fuel pin failure occurs prior to boiling onset it is at 3.7S or 5.25s into the transient depending on assumptions about the actually established strain rate. The calculated failure location is between 62 % and 75% of the fissile core height. As a consequence of the quick voiding of the upper sodium plenum, reactor shut down is initiated due to a rapid reduction of the sodium void reactivity and an initially benign fuel dispersal. When a more massive fuel pin destruction takes place about 400ms after the first fuel pin failure, the net reactivity increases again due to the superimposed effects of sodium voiding and fuel relocation. However, 20ms to 30ms later reactor shut down is initiated by a rather massive dispersal and relocation.
Results of the pure UTOP-simulations are strongly dependent on the reliability of the calculated failure time and more importantly on the calculated failure position. The most recently developed modelling approaches with SAS4A have been qualified successfully on the experimental observations of the different CABRI-programmes. These results demonstrate a large margin to failure for hollow pellet fuel pin design under transient loading. However, the success of calculations depend to a large degree on the reliability of assumptions of the dose and strain rate dependence of clad material properties. The data of these assumptions need to be
the irradiated BN-800 clad material up to dose values of 70 to 100 dpaNRT experimentally and to cover the strain rate dependency from 10"4 up to 1/s to 5/s in small steps.
UTOP/ULOF analyses
Four countries contributed to this part of the exercise namely the Russian Federation, India, France and Germany. Calculations were performed with the same code systems applied to states IV and V of the exercise. However, the Russian Federation used their newly developed CANDLE code package in addition to their GRIF-SM code. Nominal values of the reactivity feedback coefficients were used, reactivity feedback effects due to radial core expansion were neglected. Results of the calculations can be summarized as follows:
The UTOP/LOF-accident leads to coolant boiling firstly at the level of the upper sodium layer. This calculated to occur between 9.8s to ll.ls of the transient depending on the tool applied. The negative reactivity feedback due to the initial voiding of the upper sodium layer mitigates efficiently the positive reactivity feedback due to the further voiding of fissile core height. Initially the event sequence is quite similar to the one calculated at state IV of this exercise when the radial core expansion is neglected. However, the net reactivity and the normalised power level stays higher due to the super imposed external reactivity ramp rate and thus tune scales of the event sequence become smaller. It is already at about 2.1s into the boiling sequence that clad relocation starts in the SAS4A type calculations. In the GRIF- SM/CANDLE calculations this time period is considerably delayed up to 5.1s which seems to be related to the fact that GRIF-SM does not calculate actually established gap conditions, i.e.
the variation of the heat transfer coefficient between fuel clad is not taken into account appropriately. As a consequence of the clad material relocation, a positive reactivity feedback is built up which accelerates the one due to the rapidly progressing void evolution hi the core region. Another 2s to 3s later fuel pin breakup conditions are met in the high powered SAG of the MEZ. Rapidly after about half of the other SAGs enter into breakup conditions as a consequence of a rather energetic power transient which develops due to a positive reactivity ramp rate resulting from the superimposed effect of sodium boiling and clad material relocation.
At the same time of the first fuel pin break up the net reactivity stays close to prompt critical, i.e., it amounts to 0.95$ or 0.85$ respectively, depending on the model used. After first fuel pin breakup, the net reactivity rises only gradually exceeding prompt criticality only for a very limited time period of a few milliseconds (in the French calculation) because a more or less continuous dispersive fuel relocation initiates reactor shutdown after a few 100ms. However, fuel relocation seems not sufficient to lead to permanent subcriticality of the establishing core configuration.
3. GENERAL CONCLUSIONS
Transient response of an innovative BN-800 type core design to severe accidents
Evaluated consequences of the accidents considered in this comparative exercise depend on the design details given in the case set-up and on the level of detail of theoretical analyses. In
Main advantages of the as specified innovative BN-800 type core design are to be seen in providing an additional inherently activated safety margin of preventing fuel pin failure or local boiling in the domain of operational and severe transients to be considered in the design basis. These features complement well the large margin to fuel pin failure achieved already with the hollow pellet fuel pin design and a clad material providing ductility even under high dose loads. Evaluation of the impact of the as specified core design features on the core behaviour during operational transients was not part of this exercise as well as stability analyses. This would have needed other theoretical approaches to evaluate the potentially involved problems.
In the beyond design basis accident1 domain some clear advantages of the innovative core design have been identified:
Unprotected reactivity initiated accidents most probably lead to an early reactor shutdown either due to pre-failure in-pin fuel relocation and/or due to a rapid fuel dispersal after fuel pin failure in a few subassembly groups. Linear ratings at failure conditions most probably are high, i.e., at bout 1000 W/cm and more. Evaluations of the long term coolability of the established core configuration after reactivity initiated accidents were not part of this comparative exercise. They need careful consideration to evaluate potential consequences of a thermally induced subassembly to subassembly propagation.
In case of unprotected loss-of-flow accidents the main advantage of the as specified innovative core design is that it is hardly possible to approach or exceed prompt criticality in the initiating phase of the transient. At the end of most of the calculated event sequences, core configurations were established that needed transition phase analyses. This type of analyses were not part of this comparative exercise. However, they will become complicated because it remains unclear in what way permanent reactor shut down might be achieved. Release of thermal and/or mechanical energy cannot be predicted without performing appropriate analyses taking representative results of the initiation phase as initial conditions. This still needs to be done.
Conclusions from this comparative exercise hold for the specified case set-up. They need to be reviewed when some of the design features change or when more detailed evaluations lead to different input data like
• magnitude and/or spatial distributions of reactivity feedback coefficients of core materials,
• reactivity feedback effects due to radial core expansion,
• fuel pin mechanical properties, and
• if more rapidly developing consequences of control rod drive line expansion could be demonstrated.
It is felt that there are possibilities for improvement of the analyses and/or for optimisation, especially when a more realistic core design would be considered. However the comparative exercise has shown as well that consequences of these type of modifications need to be analysed carefully and in detail on a case to case basis. The use of more sophisticated and experimentally validated theoretical models would be helpful to improve the reliability of results.
Methods and codes for transient analysis
Results of this comparative exercise have shown as well that theoretical approaches chosen by India with their PINCHTRAN code package provides comprehensive results for single phase analyses but they use simplified approaches for two-phase flow. Fuel pin mechanics is not yet modeled.
The Rusian GRIF-SM code package with the complementary CANDLE-code package provides results for ULOF-type transients up to molten clad relocation. However, it is strongly recommended to couple a transient fuel pin mechanics code package to the system, to develop fuel pin failure criteria considering special features of the BN-800 fuel pin design and to extend the capabilities of the code system to describe core material relocation phenomena after fuel pin failure or breakup.
The different code versions of the SAS4A-code family available in Japan, France and Germany allow to evaluate consequences of accident initiators leading to core destruction along all stages of the initiation phase up to hexcan melting on the basis of experimentally qualified models. Even these code systems undergo continuous improvement.
In France, the pre-failure in-pin fuel relocation model EJECT is approaching completion with qualification and in Japan coupling to space time kinetics methods is far advanced. Thus, more improved analysis tools will become available in future which provide the possibility of re- evaluating the current results and to follow continuously the impact of new and/or optimised design features of innovative core designs on the results of accident analyses to be considered in the beyond design basis accident domain.
Chapter 1
SYNTHESIS OF NEUTRON PHYSICS CALCULATIONS
1.1. RUSSIAN CALCULATIONS
1.1.1. Methods and calculational models
Evaluation of the reactivity coefficients used in the subsequent analysis was made mainly on the basis of tools of the first order perturbation theory in 26-group diffusion approach. The calculations have been made using standard version of BNAB -78 data base with ARAMAKO-S system preparation of the cross section applied for justification of the BN-800 reactor design with near zero SVRE value [1.1, 1.2]. In this connection, in spite of the changes in methodology and data base which have taken place by now in Russia, standard conservative methods of applied calculation of reactivity coefficient were used as well as their models in the form which was used earlier (in 1991-1992) for their realization conformably to the design justification. In order to estimate the effect of using the different cross-section libraries some calculations were also performed with the modified version of RHEIN set developed in the framework of the former USSR-GDR bilateral cooperation [1.3,
1.4]. So for the analysis code sets realizing the above calculational method in R,Z geometry were used, namely : RADAR code using standard version of BNAB -78 data base with ARAMAKO-S system preparation of the cross section and RHEIN set with ZEMO constant preparation system for the BNAB-90 data base.
In order to evaluate criticality parameters and to make tests of the results obtained using the perturbation theory, 26-group SYNTEZ code (standard 26-group presentation with BNAB-78 data base) and 3D (GEX-Z) TRIGEX code (6 points per SA in 11-group approach[1.5]) were used. Macro data (delay neutron yield and spectra) from BNAB-78 and standard TATL libraries were used for calculation of the neutron kinetics parameters. The main reactivity coefficients were calculated using the following assumptions:
Doppler reactivity effect: Doppler constants have been evaluated (TSK/ Keff(T) - Keff(T0)
Keff(T)Keff(T0)
These values were calculated using both well known perturbation theory relationships and direct computational methods in 26-group approach in order to make corrections for scale in case of large size of temperature perturbation zone and Doppler constant correction for the sodium content change in physical and geometrical zones under consideration.
Sodium density component: Sodium density component was also evaluated using the first order perturbation theory and presented as follows:
'Na - PNa)n5KNa n
taking into account correction for the relieving of resonance cross sections (for instance [1.6, 1.7])
material thermal expansion in "k" zone, the following relationships between the linear dimension L, content p(i,k) and reactivity RE are true:
0 , 0 / i , k i , k
i k P L
In this relationship, reactivity component values determined by the perturbation theory equations are as follows:
i = -- JI
leakage in R-direction leakage in Z-direction
^, 1
-worth of main reactions
-perturbation denominator.
In such representation, reactivity effects caused by thermal expansion of the materials in axial and radial directions are evaluated using the following relationship:
Here the sodium is excluded from summation, since its expansion has already been taken into account by the sodium density components. On the other hand, the expansion model can take into account sodium displacement by the core materials expanded in radial direction.
It should be taken into consideration that the above presented model of the uniform radial expansion of the core was realized as that of an entity: «truncated cone model» with the support points in the core diagrid structure and on the SA spacer pads.
The main characteristics of the considered reactor are presented in table 1.1 and figs l.l,.1.2andl. 3. A core cartogram is shown in fig.1. 4.
For neutronic calculation the reactor calculational model in R-Z geometry was prepared. End of the run of equilibrium state was adopted. So all control rods were withdrawn from the core and placed at their upper positions. The calculational model is given in fig.l. 1.
Each sub-zone is described by two figures. The upper one is the sub-zone temperature, K; the lower one is the sub-zone number. The following designation of sub-zones is adopted: 1,2,3 - Upper part of LEZ, MEZ and HEZ, respectively; 4 - Lower axial breeder blanket; 5 - Radial breeder blanket; 6 - Sodium layer; 7 - Upper axial boron carbide shield; 9 - Control rod
Grt/
TABLE 1.1. MAIN PARAMETERS OF THE BN-800/1500 MWTH BENCHMARK CORE Core concept
Total thermal power (MW) ISadiationtime(e.f.p.d./cycles) Pitch (m)
Unit cell area (m2) Coolant flow area (m2) Active core height (m) Axial blanket height (m) Fuel assemblies
Pins/assemMy Fuel
Fuel theoretical density (gr/cm3) Fresh fuel enrichment Pu/(Pu+U)
Lower:
Midle:
Higher:
Fuel-isotopic composition (%) •.
Pu238/Pu239/Pu240/Pu241 /Pu242 U235/U236/U238
Pellet shape
dimensions (m) Pellet height (m) Inner radius (m) Outer radius (m) Axial blanket
Inner radius (m) Outer radius (m) Clad
inner radius (m) outer radius (m)
Central pins wire diameter (m) Near-wall pins wire diameter (m) Steel slug diameter (m)
Number of slugs
Heterogeneous 13 Enrichments 1500
140x3
Fissile Fertile 0.1006
0.008764
0.002403 0.001438 0.851 1.58 0.355
181/138/162 84 127 37
(U,Pu)Ol98 UO2
10.97 10.69 20.08%
23.17%
27.35%
0.0/60.0/25.0/10.9/4.1 0.4/0.0/99.6
Chamferred edges 0.00025x0.00025
0.008 0.000825 0.0 0.0028 0.0068
0.0 0.002825
0.0029 0.0033 0.00115
0.0016 36
0.0066 0.0070
0.0006x0.0013 0.0035
18
DH\DR (sm) 70.00
31.18
25.15
35.21
5.00
28.00
28.00
29.10
35.50
67.00
70.00 1 1 25.05
900 16 900 17 900 7 900 6 900
24 1500
1 1500
18 1500
21 1200
4 900 14 900~
16 1 1 3.14
900 16 900 11 900 11 900~
11 900 11 1500
9 1500
9 1500
9 1200
9 900 9 900 16
17.00 900 16 900 17 900 7 900 6 900 24 1500
1 1500
18 1500
21 1200
4 900 14 900 16
1.82 900 16 900 12 900 12 900 12 900 12 1500 9 1500
9 1500
9
TzTxT
9 900 9 900
16 I 5.43
900 16 900 17 900 7 900 6 900 24 1500
1 1500
18 1500
21 1200
4 900 14 900 16
1.58 900
16 900 12 900 12 900 12 900 12 1500
9 1500
9 1500
9 1200
9 900
9 900"
16
15.21 900
16 900 17 900 7 900 6 900 24 1500
1 1500
18
"T500~
21 1200
4 900 14 900 16
2.38 900 16 900 11 900 11 900 11 900 11 1500 9 1500
9 1500 '
9 1200
9 900~
9 900 16
5.11 900 16 900 17 900 7 900 6 900~
24 1500
1 1500
18 1500
21 1200
4 900
14 900 16
21.95 900
16 900 17 900 7
900 6 900 24 1500
2 1500
19 1500
22 1200
4 900 '
14 900
16 I 20.73
900 16 900 17 900 7 900 6 900
24 1500
3 1500
20 1500
23 1200
4 900 14 900 16
1 9.44 900 16 900 17 1200 5 1200
5 1200
5 1200
5 1200
5 1200
5 1200
4 900 "
14 900 16
9.40 900 16 900 17 900 15 900 15 900 15 900 15 900 15 900 15 900 15 900 14 900 16
1 18.70| 30.00
900 16 900 17 900~
8 900 8 900 '
8 900~
8 900 8 900
8 900 8 900
14 900 16
900 16 900 16 900 16 900 16 900 16 900 16 900 16 900 16 900 16 900 16 900 16
HEZ, respectively; 21,22,23 - Lower part of LEZ, MEZ and HEZ, respectively; 24 - Pin steel plugs.
Nuclear concentrations in 1024nucl/cm3 for subzones are listed in table 1. Al Appendix.
12
12
70.00
31.18
ax.shield
35.21 Ma-layer 5.00
28.00 upper fuel 28.00 midlefuel
29.10 kHMTfuei
35.50 ax. blanket
67.00 plenum
70.0
UOj
b4c
FIG. 1.3. Axial structure and geometry for fissile, fertile and c.r. assemblies for the neutronic calculations.
21 3 3 4 5 61 6 7 7 7
2 3 3 4 5 6 « 71 7l 7 3 4 5 T • T « T 7 T 7 T r
Lower Enrichment Fuel
2 I Midle Enrichment Fuel High Enrichment Fuel Ferttes
SS-Shield
^•t^
0 0
0
0
ReflectorsCompensating Rods Scram/Passive Scram Rods
FIG. 1.4. One 60°- sector cross-section lay out for the BN-800 /1500 MWth benchmark core.
1.1.2. Results of calculations
Criticality parameters: Three different approaches that were used for calculations gave the following values of effective multiplication factor:
Neutron components in the reactor (finite difference method) for the first method are presented below:
capture fission
multiplication N-2N
leakage
capture fraction leakage fraction
fission neutron worth in the reactor, including
LEZ MEZ HEZ
radial blanket
0.3028E+8 0.1603E+8 0.4651E+8 0.5850E+5 0.2609E+6 0.9944 0.0056 0.3800E+9
1.69E+8 1.19E+8 8.40E+7 4.06E+6
Neutron kinetics functionals: The main neutron kinetics functionals are given in table 1.
2 using delay neutron parameters based on BNAB and TATL data libraries in the framework of one computation code (RHEIN). The diversity of group values ZP and total value (3eff is caused mainly by the applied version of delay neutron parameters. Maximum difference is determined for the 6-th group, first of all owing to the high plutonium isotopes. In this case, it is to be noted that the absolute values of the delay neutron yield for 241Pu and 242Pu in the BNAB library corrected with account of the results of measurement of the plutonium critical assemblies.
TABLE 1.2. NEUTRONICS PARAMETERS
BNAB Library (Russia) Group
U-235 U-238 Pu-239 Pu-240 Pu-241 Pu-242
ip
peff
Lp, sec A-i, I/sec
U-235 U-238 Pu-239 Pu-240 Pu-241 Pu-242
sp
peff Lp, sec
Xi, I/sec
p^ff 0.28 IE-5 0.172E-4 0.4559E-4 0.4936E-5 0.6013E-5 0.1839E-6 7.67E-5
0,0129
0.2784E-5 0.1932E-4 0.4525E-4 0.528 IE-5 0.1193E-4 0.7824E-6 8.5343E-5
0.01340
p2eff 0.166E-4 0.1904E-3 0.3539E-3 0.5060E-4 0.1469E-3 0.9257E-5 7.68E-4
0,0311 TATL 0.1460E-4 0.1585E-3 0.3019E-3 0.427 IE-4 0.1506E-3 0.9349E-5 6.7765E-4
0.030781
P3eff p4eff
0.145E-4 0.3158E-4 0.222E-3 0.5342E-3 0.2686E-3 0.4098E-3 0.350 IE-4 0.6422E-4 0.1088E-3 0.246 IE-3 0.7516E-5 0.1933E-4 6.56E-4 1.31E-3
0.3563E-2 0.4418E-6(R4JDAR)
0,134 0,331
Library (Russia) 0.1387E-4 0.3176E-4 0.1813E-3 0.5444E-3 0.2234E-3 0.4145E-3 0.2487E-4 0.5525E-4 0.9309E-4 0.2317E-3 0.4943E-5 0.1304E-4 5.4146E-4 1.2906E-3
3.6208E-3 4.4776E-7 (RHEIN) 0.11742 0.30824
p5erf 0.983E-5 0.3073E-3 0.1274E-3 0.2323E-4 0.1145E-3 0.1015E-4 5.92E-4
1,260
0.1291E-4 0.3558E-3 0.2146E-3 0.2990E- 0.1304E-3 0.8984E-5 7.5260E-4
1.2418
P^
0.2011E-5 0.1033E-3 0.4386E-4 0.5360E-5 0.1013E-4 0.4682E-6 1.65E-4
3,210
0.5413E-5 0.1452E-3 0.6522E-4 0.9155E-5 0.4526E-4 0.2869E-5 2.7316E-4
2.9500
Sodium void and density reactivity effects: The results of calculations of SVRE as a function of sodium fraction in the different zones using SYNTEZ code are presented in the table 1. 3.
One can see from table 1. 3 that the effect depends on temperature, changing non-linearly with sodium fraction.
As far as "interaction effect" between single voided fuel zones is concern it turns out that the simple sum of the single fuel zone reactivity worths under-estimates the positive actual value for the case of fully voided core by «5%, and the simple sum of the reactivity worths for all fuel zones and sodium layer zone differs from directly calculated value by 26%
for T=900K and almost by 3 times for T=2100K.
To complete the sodium void effect analysis it is necessary to make some comments with respect to the results presented in the "Input data" (table 1. A.2, appendix). These data are the result of normalization of sodium efficiency spatial distribution obtained using perturbation theory on the directly calculated results. Sodium efficiency values in the bottom axial blanket and in the core have been normalized to the SVRE value in the core while the sodium efficiency in the above core area has been normalized to the sodium plenum efficiency. It is to be noted that SVRE for "Input Data.." was calculated under the condition that sodium was not removed from control rod channel but only from subassemblies.
Doppler reactivity: As it follows from table 1.4 1-st order perturbation theory calculations
